package bisq.core.xmr.org.nem.core.crypto.ed25519.arithmetic;

import bisq.core.xmr.org.nem.core.utils.ArrayUtils;
import bisq.core.xmr.org.nem.core.utils.HexEncoder;

import java.util.Arrays;

/**
 * Represents a field element of the finite field with p=2^255-19 elements.
 * The value of the field element is held in 2^8 bit representation, i.e. in a byte array.
 * The length of the array must be 32 or 64.
 */
public class Ed25519EncodedFieldElement {
    private final byte[] zero;
    private final byte[] values;

    /**
     * Creates a new encoded field element.
     *
     * @param values The byte array that holds the values.
     */
    public Ed25519EncodedFieldElement(final byte[] values) {
        switch (values.length) {
            case 32:
                this.zero = Ed25519Field.ZERO_SHORT;
                break;
            case 64:
                this.zero = Ed25519Field.ZERO_LONG;
                break;
            default:
                throw new IllegalArgumentException("Invalid 2^8 bit representation.");
        }

        this.values = values;
    }

    /**
     * Gets the underlying byte array.
     *
     * @return The byte array.
     */
    public byte[] getRaw() {
        return this.values;
    }

    /**
     * Return true if this is in {1,3,5,...,q-2}
     * Return false if this is in {0,2,4,...,q-1}
     * <br>
     * Preconditions:
     * |x| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
     *
     * @return true if this is in {1,3,5,...,q-2}, false otherwise.
     */
    public boolean isNegative() {
        return (this.values[0] & 1) != 0;
    }

    /**
     * Gets a value indicating whether or not the field element is non-zero.
     *
     * @return 1 if it is non-zero, 0 otherwise.
     */
    public boolean isNonZero() {
        return 0 == ArrayUtils.isEqualConstantTime(this.values, this.zero);
    }

    /**
     * Decodes this encoded (32 byte) representation to a field element in its 10 byte 2^25.5 representation.
     * The most significant bit is discarded.
     *
     * @return The field element in its 2^25.5 bit representation.
     */
    public Ed25519FieldElement decode() {
        long h0 = fourBytesToLong(this.values, 0);
        long h1 = threeBytesToLong(this.values, 4) << 6;
        long h2 = threeBytesToLong(this.values, 7) << 5;
        long h3 = threeBytesToLong(this.values, 10) << 3;
        long h4 = threeBytesToLong(this.values, 13) << 2;
        long h5 = fourBytesToLong(this.values, 16);
        long h6 = threeBytesToLong(this.values, 20) << 7;
        long h7 = threeBytesToLong(this.values, 23) << 5;
        long h8 = threeBytesToLong(this.values, 26) << 4;
        long h9 = (threeBytesToLong(this.values, 29) & 0x7FFFFF) << 2;
        final long carry0;
        final long carry1;
        final long carry2;
        final long carry3;
        final long carry4;
        final long carry5;
        final long carry6;
        final long carry7;
        final long carry8;
        final long carry9;

        // Remember: 2^255 congruent 19 modulo p
        carry9 = (h9 + (long) (1 << 24)) >> 25;
        h0 += carry9 * 19;
        h9 -= carry9 << 25;
        carry1 = (h1 + (long) (1 << 24)) >> 25;
        h2 += carry1;
        h1 -= carry1 << 25;
        carry3 = (h3 + (long) (1 << 24)) >> 25;
        h4 += carry3;
        h3 -= carry3 << 25;
        carry5 = (h5 + (long) (1 << 24)) >> 25;
        h6 += carry5;
        h5 -= carry5 << 25;
        carry7 = (h7 + (long) (1 << 24)) >> 25;
        h8 += carry7;
        h7 -= carry7 << 25;

        carry0 = (h0 + (long) (1 << 25)) >> 26;
        h1 += carry0;
        h0 -= carry0 << 26;
        carry2 = (h2 + (long) (1 << 25)) >> 26;
        h3 += carry2;
        h2 -= carry2 << 26;
        carry4 = (h4 + (long) (1 << 25)) >> 26;
        h5 += carry4;
        h4 -= carry4 << 26;
        carry6 = (h6 + (long) (1 << 25)) >> 26;
        h7 += carry6;
        h6 -= carry6 << 26;
        carry8 = (h8 + (long) (1 << 25)) >> 26;
        h9 += carry8;
        h8 -= carry8 << 26;

        final int[] h = new int[10];
        h[0] = (int) h0;
        h[1] = (int) h1;
        h[2] = (int) h2;
        h[3] = (int) h3;
        h[4] = (int) h4;
        h[5] = (int) h5;
        h[6] = (int) h6;
        h[7] = (int) h7;
        h[8] = (int) h8;
        h[9] = (int) h9;

        return new Ed25519FieldElement(h);
    }

    /**
     * Reduces this encoded field element (64 bytes) modulo the group order q.
     *
     * @return Encoded field element (32 bytes).
     */
    public Ed25519EncodedFieldElement modQ() {
        // s0, ..., s22 have 21 bits, s23 has 29 bits
        long s0 = 0x1FFFFF & threeBytesToLong(this.values, 0);
        long s1 = 0x1FFFFF & (fourBytesToLong(this.values, 2) >> 5);
        long s2 = 0x1FFFFF & (threeBytesToLong(this.values, 5) >> 2);
        long s3 = 0x1FFFFF & (fourBytesToLong(this.values, 7) >> 7);
        long s4 = 0x1FFFFF & (fourBytesToLong(this.values, 10) >> 4);
        long s5 = 0x1FFFFF & (threeBytesToLong(this.values, 13) >> 1);
        long s6 = 0x1FFFFF & (fourBytesToLong(this.values, 15) >> 6);
        long s7 = 0x1FFFFF & (threeBytesToLong(this.values, 18) >> 3);
        long s8 = 0x1FFFFF & threeBytesToLong(this.values, 21);
        long s9 = 0x1FFFFF & (fourBytesToLong(this.values, 23) >> 5);
        long s10 = 0x1FFFFF & (threeBytesToLong(this.values, 26) >> 2);
        long s11 = 0x1FFFFF & (fourBytesToLong(this.values, 28) >> 7);
        long s12 = 0x1FFFFF & (fourBytesToLong(this.values, 31) >> 4);
        long s13 = 0x1FFFFF & (threeBytesToLong(this.values, 34) >> 1);
        long s14 = 0x1FFFFF & (fourBytesToLong(this.values, 36) >> 6);
        long s15 = 0x1FFFFF & (threeBytesToLong(this.values, 39) >> 3);
        long s16 = 0x1FFFFF & threeBytesToLong(this.values, 42);
        long s17 = 0x1FFFFF & (fourBytesToLong(this.values, 44) >> 5);
        final long s18 = 0x1FFFFF & (threeBytesToLong(this.values, 47) >> 2);
        final long s19 = 0x1FFFFF & (fourBytesToLong(this.values, 49) >> 7);
        final long s20 = 0x1FFFFF & (fourBytesToLong(this.values, 52) >> 4);
        final long s21 = 0x1FFFFF & (threeBytesToLong(this.values, 55) >> 1);
        final long s22 = 0x1FFFFF & (fourBytesToLong(this.values, 57) >> 6);
        final long s23 = (fourBytesToLong(this.values, 60) >> 3);
        long carry0;
        long carry1;
        long carry2;
        long carry3;
        long carry4;
        long carry5;
        long carry6;
        long carry7;
        long carry8;
        long carry9;
        long carry10;
        long carry11;
        final long carry12;
        final long carry13;
        final long carry14;
        final long carry15;
        final long carry16;

        /**
         * Lots of magic numbers :)
         * To understand what's going on below, note that
         *
         * (1) q = 2^252 + q0 where q0 = 27742317777372353535851937790883648493.
         * (2) s11 is the coefficient of 2^(11*21), s23 is the coefficient of 2^(^23*21) and 2^252 = 2^((23-11) * 21)).
         * (3) 2^252 congruent -q0 modulo q.
         * (4) -q0 = 666643 * 2^0 + 470296 * 2^21 + 654183 * 2^(2*21) - 997805 * 2^(3*21) + 136657 * 2^(4*21) - 683901 * 2^(5*21)
         *
         * Thus
         * s23 * 2^(23*11) = s23 * 2^(12*21) * 2^(11*21) = s3 * 2^252 * 2^(11*21) congruent
         * s23 * (666643 * 2^0 + 470296 * 2^21 + 654183 * 2^(2*21) - 997805 * 2^(3*21) + 136657 * 2^(4*21) - 683901 * 2^(5*21)) * 2^(11*21) modulo q =
         * s23 * (666643 * 2^(11*21) + 470296 * 2^(12*21) + 654183 * 2^(13*21) - 997805 * 2^(14*21) + 136657 * 2^(15*21) - 683901 * 2^(16*21)).
         *
         * The same procedure is then applied for s22,...,s18.
         */
        s11 += s23 * 666643;
        s12 += s23 * 470296;
        s13 += s23 * 654183;
        s14 -= s23 * 997805;
        s15 += s23 * 136657;
        s16 -= s23 * 683901;

        s10 += s22 * 666643;
        s11 += s22 * 470296;
        s12 += s22 * 654183;
        s13 -= s22 * 997805;
        s14 += s22 * 136657;
        s15 -= s22 * 683901;

        s9 += s21 * 666643;
        s10 += s21 * 470296;
        s11 += s21 * 654183;
        s12 -= s21 * 997805;
        s13 += s21 * 136657;
        s14 -= s21 * 683901;

        s8 += s20 * 666643;
        s9 += s20 * 470296;
        s10 += s20 * 654183;
        s11 -= s20 * 997805;
        s12 += s20 * 136657;
        s13 -= s20 * 683901;

        s7 += s19 * 666643;
        s8 += s19 * 470296;
        s9 += s19 * 654183;
        s10 -= s19 * 997805;
        s11 += s19 * 136657;
        s12 -= s19 * 683901;

        s6 += s18 * 666643;
        s7 += s18 * 470296;
        s8 += s18 * 654183;
        s9 -= s18 * 997805;
        s10 += s18 * 136657;
        s11 -= s18 * 683901;

        /**
         * Time to reduce the coefficient in order not to get an overflow.
         */
        carry6 = (s6 + (1 << 20)) >> 21;
        s7 += carry6;
        s6 -= carry6 << 21;
        carry8 = (s8 + (1 << 20)) >> 21;
        s9 += carry8;
        s8 -= carry8 << 21;
        carry10 = (s10 + (1 << 20)) >> 21;
        s11 += carry10;
        s10 -= carry10 << 21;
        carry12 = (s12 + (1 << 20)) >> 21;
        s13 += carry12;
        s12 -= carry12 << 21;
        carry14 = (s14 + (1 << 20)) >> 21;
        s15 += carry14;
        s14 -= carry14 << 21;
        carry16 = (s16 + (1 << 20)) >> 21;
        s17 += carry16;
        s16 -= carry16 << 21;

        carry7 = (s7 + (1 << 20)) >> 21;
        s8 += carry7;
        s7 -= carry7 << 21;
        carry9 = (s9 + (1 << 20)) >> 21;
        s10 += carry9;
        s9 -= carry9 << 21;
        carry11 = (s11 + (1 << 20)) >> 21;
        s12 += carry11;
        s11 -= carry11 << 21;
        carry13 = (s13 + (1 << 20)) >> 21;
        s14 += carry13;
        s13 -= carry13 << 21;
        carry15 = (s15 + (1 << 20)) >> 21;
        s16 += carry15;
        s15 -= carry15 << 21;

        /**
         * Continue with above procedure.
         */
        s5 += s17 * 666643;
        s6 += s17 * 470296;
        s7 += s17 * 654183;
        s8 -= s17 * 997805;
        s9 += s17 * 136657;
        s10 -= s17 * 683901;

        s4 += s16 * 666643;
        s5 += s16 * 470296;
        s6 += s16 * 654183;
        s7 -= s16 * 997805;
        s8 += s16 * 136657;
        s9 -= s16 * 683901;

        s3 += s15 * 666643;
        s4 += s15 * 470296;
        s5 += s15 * 654183;
        s6 -= s15 * 997805;
        s7 += s15 * 136657;
        s8 -= s15 * 683901;

        s2 += s14 * 666643;
        s3 += s14 * 470296;
        s4 += s14 * 654183;
        s5 -= s14 * 997805;
        s6 += s14 * 136657;
        s7 -= s14 * 683901;

        s1 += s13 * 666643;
        s2 += s13 * 470296;
        s3 += s13 * 654183;
        s4 -= s13 * 997805;
        s5 += s13 * 136657;
        s6 -= s13 * 683901;

        s0 += s12 * 666643;
        s1 += s12 * 470296;
        s2 += s12 * 654183;
        s3 -= s12 * 997805;
        s4 += s12 * 136657;
        s5 -= s12 * 683901;
        s12 = 0;

        /**
         * Reduce coefficients again.
         */
        carry0 = (s0 + (1 << 20)) >> 21;
        s1 += carry0;
        s0 -= carry0 << 21;
        carry2 = (s2 + (1 << 20)) >> 21;
        s3 += carry2;
        s2 -= carry2 << 21;
        carry4 = (s4 + (1 << 20)) >> 21;
        s5 += carry4;
        s4 -= carry4 << 21;
        carry6 = (s6 + (1 << 20)) >> 21;
        s7 += carry6;
        s6 -= carry6 << 21;
        carry8 = (s8 + (1 << 20)) >> 21;
        s9 += carry8;
        s8 -= carry8 << 21;
        carry10 = (s10 + (1 << 20)) >> 21;
        s11 += carry10;
        s10 -= carry10 << 21;

        carry1 = (s1 + (1 << 20)) >> 21;
        s2 += carry1;
        s1 -= carry1 << 21;
        carry3 = (s3 + (1 << 20)) >> 21;
        s4 += carry3;
        s3 -= carry3 << 21;
        carry5 = (s5 + (1 << 20)) >> 21;
        s6 += carry5;
        s5 -= carry5 << 21;
        carry7 = (s7 + (1 << 20)) >> 21;
        s8 += carry7;
        s7 -= carry7 << 21;
        carry9 = (s9 + (1 << 20)) >> 21;
        s10 += carry9;
        s9 -= carry9 << 21;
        carry11 = (s11 + (1 << 20)) >> 21;
        s12 += carry11;
        s11 -= carry11 << 21;

        s0 += s12 * 666643;
        s1 += s12 * 470296;
        s2 += s12 * 654183;
        s3 -= s12 * 997805;
        s4 += s12 * 136657;
        s5 -= s12 * 683901;
        s12 = 0;

        carry0 = s0 >> 21;
        s1 += carry0;
        s0 -= carry0 << 21;
        carry1 = s1 >> 21;
        s2 += carry1;
        s1 -= carry1 << 21;
        carry2 = s2 >> 21;
        s3 += carry2;
        s2 -= carry2 << 21;
        carry3 = s3 >> 21;
        s4 += carry3;
        s3 -= carry3 << 21;
        carry4 = s4 >> 21;
        s5 += carry4;
        s4 -= carry4 << 21;
        carry5 = s5 >> 21;
        s6 += carry5;
        s5 -= carry5 << 21;
        carry6 = s6 >> 21;
        s7 += carry6;
        s6 -= carry6 << 21;
        carry7 = s7 >> 21;
        s8 += carry7;
        s7 -= carry7 << 21;
        carry8 = s8 >> 21;
        s9 += carry8;
        s8 -= carry8 << 21;
        carry9 = s9 >> 21;
        s10 += carry9;
        s9 -= carry9 << 21;
        carry10 = s10 >> 21;
        s11 += carry10;
        s10 -= carry10 << 21;
        carry11 = s11 >> 21;
        s12 += carry11;
        s11 -= carry11 << 21;

        s0 += s12 * 666643;
        s1 += s12 * 470296;
        s2 += s12 * 654183;
        s3 -= s12 * 997805;
        s4 += s12 * 136657;
        s5 -= s12 * 683901;

        carry0 = s0 >> 21;
        s1 += carry0;
        s0 -= carry0 << 21;
        carry1 = s1 >> 21;
        s2 += carry1;
        s1 -= carry1 << 21;
        carry2 = s2 >> 21;
        s3 += carry2;
        s2 -= carry2 << 21;
        carry3 = s3 >> 21;
        s4 += carry3;
        s3 -= carry3 << 21;
        carry4 = s4 >> 21;
        s5 += carry4;
        s4 -= carry4 << 21;
        carry5 = s5 >> 21;
        s6 += carry5;
        s5 -= carry5 << 21;
        carry6 = s6 >> 21;
        s7 += carry6;
        s6 -= carry6 << 21;
        carry7 = s7 >> 21;
        s8 += carry7;
        s7 -= carry7 << 21;
        carry8 = s8 >> 21;
        s9 += carry8;
        s8 -= carry8 << 21;
        carry9 = s9 >> 21;
        s10 += carry9;
        s9 -= carry9 << 21;
        carry10 = s10 >> 21;
        s11 += carry10;
        s10 -= carry10 << 21;

        // s0, ..., s11 got 21 bits each.
        final byte[] result = new byte[32];
        result[0] = (byte) (s0);
        result[1] = (byte) (s0 >> 8);
        result[2] = (byte) ((s0 >> 16) | (s1 << 5));
        result[3] = (byte) (s1 >> 3);
        result[4] = (byte) (s1 >> 11);
        result[5] = (byte) ((s1 >> 19) | (s2 << 2));
        result[6] = (byte) (s2 >> 6);
        result[7] = (byte) ((s2 >> 14) | (s3 << 7));
        result[8] = (byte) (s3 >> 1);
        result[9] = (byte) (s3 >> 9);
        result[10] = (byte) ((s3 >> 17) | (s4 << 4));
        result[11] = (byte) (s4 >> 4);
        result[12] = (byte) (s4 >> 12);
        result[13] = (byte) ((s4 >> 20) | (s5 << 1));
        result[14] = (byte) (s5 >> 7);
        result[15] = (byte) ((s5 >> 15) | (s6 << 6));
        result[16] = (byte) (s6 >> 2);
        result[17] = (byte) (s6 >> 10);
        result[18] = (byte) ((s6 >> 18) | (s7 << 3));
        result[19] = (byte) (s7 >> 5);
        result[20] = (byte) (s7 >> 13);
        result[21] = (byte) (s8);
        result[22] = (byte) (s8 >> 8);
        result[23] = (byte) ((s8 >> 16) | (s9 << 5));
        result[24] = (byte) (s9 >> 3);
        result[25] = (byte) (s9 >> 11);
        result[26] = (byte) ((s9 >> 19) | (s10 << 2));
        result[27] = (byte) (s10 >> 6);
        result[28] = (byte) ((s10 >> 14) | (s11 << 7));
        result[29] = (byte) (s11 >> 1);
        result[30] = (byte) (s11 >> 9);
        result[31] = (byte) (s11 >> 17);

        return new Ed25519EncodedFieldElement(result);
    }

    /**
     * Multiplies this encoded field element with another and adds a third.
     * The result is reduced modulo the group order.
     * <br>
     * See the comments in the method modQ() for an explanation of the algorithm.
     *
     * @param b The encoded field element which is multiplied with this.
     * @param c The third encoded field element which is added.
     * @return The encoded field element (32 bytes).
     */
    public Ed25519EncodedFieldElement multiplyAndAddModQ(final Ed25519EncodedFieldElement b,
                                                         final Ed25519EncodedFieldElement c) {
        final long a0 = 0x1FFFFF & threeBytesToLong(this.values, 0);
        final long a1 = 0x1FFFFF & (fourBytesToLong(this.values, 2) >> 5);
        final long a2 = 0x1FFFFF & (threeBytesToLong(this.values, 5) >> 2);
        final long a3 = 0x1FFFFF & (fourBytesToLong(this.values, 7) >> 7);
        final long a4 = 0x1FFFFF & (fourBytesToLong(this.values, 10) >> 4);
        final long a5 = 0x1FFFFF & (threeBytesToLong(this.values, 13) >> 1);
        final long a6 = 0x1FFFFF & (fourBytesToLong(this.values, 15) >> 6);
        final long a7 = 0x1FFFFF & (threeBytesToLong(this.values, 18) >> 3);
        final long a8 = 0x1FFFFF & threeBytesToLong(this.values, 21);
        final long a9 = 0x1FFFFF & (fourBytesToLong(this.values, 23) >> 5);
        final long a10 = 0x1FFFFF & (threeBytesToLong(this.values, 26) >> 2);
        final long a11 = (fourBytesToLong(this.values, 28) >> 7);
        final long b0 = 0x1FFFFF & threeBytesToLong(b.values, 0);
        final long b1 = 0x1FFFFF & (fourBytesToLong(b.values, 2) >> 5);
        final long b2 = 0x1FFFFF & (threeBytesToLong(b.values, 5) >> 2);
        final long b3 = 0x1FFFFF & (fourBytesToLong(b.values, 7) >> 7);
        final long b4 = 0x1FFFFF & (fourBytesToLong(b.values, 10) >> 4);
        final long b5 = 0x1FFFFF & (threeBytesToLong(b.values, 13) >> 1);
        final long b6 = 0x1FFFFF & (fourBytesToLong(b.values, 15) >> 6);
        final long b7 = 0x1FFFFF & (threeBytesToLong(b.values, 18) >> 3);
        final long b8 = 0x1FFFFF & threeBytesToLong(b.values, 21);
        final long b9 = 0x1FFFFF & (fourBytesToLong(b.values, 23) >> 5);
        final long b10 = 0x1FFFFF & (threeBytesToLong(b.values, 26) >> 2);
        final long b11 = (fourBytesToLong(b.values, 28) >> 7);
        final long c0 = 0x1FFFFF & threeBytesToLong(c.values, 0);
        final long c1 = 0x1FFFFF & (fourBytesToLong(c.values, 2) >> 5);
        final long c2 = 0x1FFFFF & (threeBytesToLong(c.values, 5) >> 2);
        final long c3 = 0x1FFFFF & (fourBytesToLong(c.values, 7) >> 7);
        final long c4 = 0x1FFFFF & (fourBytesToLong(c.values, 10) >> 4);
        final long c5 = 0x1FFFFF & (threeBytesToLong(c.values, 13) >> 1);
        final long c6 = 0x1FFFFF & (fourBytesToLong(c.values, 15) >> 6);
        final long c7 = 0x1FFFFF & (threeBytesToLong(c.values, 18) >> 3);
        final long c8 = 0x1FFFFF & threeBytesToLong(c.values, 21);
        final long c9 = 0x1FFFFF & (fourBytesToLong(c.values, 23) >> 5);
        final long c10 = 0x1FFFFF & (threeBytesToLong(c.values, 26) >> 2);
        final long c11 = (fourBytesToLong(c.values, 28) >> 7);
        long s0;
        long s1;
        long s2;
        long s3;
        long s4;
        long s5;
        long s6;
        long s7;
        long s8;
        long s9;
        long s10;
        long s11;
        long s12;
        long s13;
        long s14;
        long s15;
        long s16;
        long s17;
        long s18;
        long s19;
        long s20;
        long s21;
        long s22;
        long s23;
        long carry0;
        long carry1;
        long carry2;
        long carry3;
        long carry4;
        long carry5;
        long carry6;
        long carry7;
        long carry8;
        long carry9;
        long carry10;
        long carry11;
        long carry12;
        long carry13;
        long carry14;
        long carry15;
        long carry16;
        final long carry17;
        final long carry18;
        final long carry19;
        final long carry20;
        final long carry21;
        final long carry22;

        s0 = c0 + a0 * b0;
        s1 = c1 + a0 * b1 + a1 * b0;
        s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
        s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
        s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
        s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
        s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
        s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
        s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
        s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
        s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
        s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
        s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
        s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
        s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
        s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
        s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
        s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
        s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
        s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
        s20 = a9 * b11 + a10 * b10 + a11 * b9;
        s21 = a10 * b11 + a11 * b10;
        s22 = a11 * b11;
        s23 = 0;

        carry0 = (s0 + (1 << 20)) >> 21;
        s1 += carry0;
        s0 -= carry0 << 21;
        carry2 = (s2 + (1 << 20)) >> 21;
        s3 += carry2;
        s2 -= carry2 << 21;
        carry4 = (s4 + (1 << 20)) >> 21;
        s5 += carry4;
        s4 -= carry4 << 21;
        carry6 = (s6 + (1 << 20)) >> 21;
        s7 += carry6;
        s6 -= carry6 << 21;
        carry8 = (s8 + (1 << 20)) >> 21;
        s9 += carry8;
        s8 -= carry8 << 21;
        carry10 = (s10 + (1 << 20)) >> 21;
        s11 += carry10;
        s10 -= carry10 << 21;
        carry12 = (s12 + (1 << 20)) >> 21;
        s13 += carry12;
        s12 -= carry12 << 21;
        carry14 = (s14 + (1 << 20)) >> 21;
        s15 += carry14;
        s14 -= carry14 << 21;
        carry16 = (s16 + (1 << 20)) >> 21;
        s17 += carry16;
        s16 -= carry16 << 21;
        carry18 = (s18 + (1 << 20)) >> 21;
        s19 += carry18;
        s18 -= carry18 << 21;
        carry20 = (s20 + (1 << 20)) >> 21;
        s21 += carry20;
        s20 -= carry20 << 21;
        carry22 = (s22 + (1 << 20)) >> 21;
        s23 += carry22;
        s22 -= carry22 << 21;

        carry1 = (s1 + (1 << 20)) >> 21;
        s2 += carry1;
        s1 -= carry1 << 21;
        carry3 = (s3 + (1 << 20)) >> 21;
        s4 += carry3;
        s3 -= carry3 << 21;
        carry5 = (s5 + (1 << 20)) >> 21;
        s6 += carry5;
        s5 -= carry5 << 21;
        carry7 = (s7 + (1 << 20)) >> 21;
        s8 += carry7;
        s7 -= carry7 << 21;
        carry9 = (s9 + (1 << 20)) >> 21;
        s10 += carry9;
        s9 -= carry9 << 21;
        carry11 = (s11 + (1 << 20)) >> 21;
        s12 += carry11;
        s11 -= carry11 << 21;
        carry13 = (s13 + (1 << 20)) >> 21;
        s14 += carry13;
        s13 -= carry13 << 21;
        carry15 = (s15 + (1 << 20)) >> 21;
        s16 += carry15;
        s15 -= carry15 << 21;
        carry17 = (s17 + (1 << 20)) >> 21;
        s18 += carry17;
        s17 -= carry17 << 21;
        carry19 = (s19 + (1 << 20)) >> 21;
        s20 += carry19;
        s19 -= carry19 << 21;
        carry21 = (s21 + (1 << 20)) >> 21;
        s22 += carry21;
        s21 -= carry21 << 21;

        s11 += s23 * 666643;
        s12 += s23 * 470296;
        s13 += s23 * 654183;
        s14 -= s23 * 997805;
        s15 += s23 * 136657;
        s16 -= s23 * 683901;

        s10 += s22 * 666643;
        s11 += s22 * 470296;
        s12 += s22 * 654183;
        s13 -= s22 * 997805;
        s14 += s22 * 136657;
        s15 -= s22 * 683901;

        s9 += s21 * 666643;
        s10 += s21 * 470296;
        s11 += s21 * 654183;
        s12 -= s21 * 997805;
        s13 += s21 * 136657;
        s14 -= s21 * 683901;

        s8 += s20 * 666643;
        s9 += s20 * 470296;
        s10 += s20 * 654183;
        s11 -= s20 * 997805;
        s12 += s20 * 136657;
        s13 -= s20 * 683901;

        s7 += s19 * 666643;
        s8 += s19 * 470296;
        s9 += s19 * 654183;
        s10 -= s19 * 997805;
        s11 += s19 * 136657;
        s12 -= s19 * 683901;

        s6 += s18 * 666643;
        s7 += s18 * 470296;
        s8 += s18 * 654183;
        s9 -= s18 * 997805;
        s10 += s18 * 136657;
        s11 -= s18 * 683901;

        carry6 = (s6 + (1 << 20)) >> 21;
        s7 += carry6;
        s6 -= carry6 << 21;
        carry8 = (s8 + (1 << 20)) >> 21;
        s9 += carry8;
        s8 -= carry8 << 21;
        carry10 = (s10 + (1 << 20)) >> 21;
        s11 += carry10;
        s10 -= carry10 << 21;
        carry12 = (s12 + (1 << 20)) >> 21;
        s13 += carry12;
        s12 -= carry12 << 21;
        carry14 = (s14 + (1 << 20)) >> 21;
        s15 += carry14;
        s14 -= carry14 << 21;
        carry16 = (s16 + (1 << 20)) >> 21;
        s17 += carry16;
        s16 -= carry16 << 21;

        carry7 = (s7 + (1 << 20)) >> 21;
        s8 += carry7;
        s7 -= carry7 << 21;
        carry9 = (s9 + (1 << 20)) >> 21;
        s10 += carry9;
        s9 -= carry9 << 21;
        carry11 = (s11 + (1 << 20)) >> 21;
        s12 += carry11;
        s11 -= carry11 << 21;
        carry13 = (s13 + (1 << 20)) >> 21;
        s14 += carry13;
        s13 -= carry13 << 21;
        carry15 = (s15 + (1 << 20)) >> 21;
        s16 += carry15;
        s15 -= carry15 << 21;

        s5 += s17 * 666643;
        s6 += s17 * 470296;
        s7 += s17 * 654183;
        s8 -= s17 * 997805;
        s9 += s17 * 136657;
        s10 -= s17 * 683901;

        s4 += s16 * 666643;
        s5 += s16 * 470296;
        s6 += s16 * 654183;
        s7 -= s16 * 997805;
        s8 += s16 * 136657;
        s9 -= s16 * 683901;

        s3 += s15 * 666643;
        s4 += s15 * 470296;
        s5 += s15 * 654183;
        s6 -= s15 * 997805;
        s7 += s15 * 136657;
        s8 -= s15 * 683901;

        s2 += s14 * 666643;
        s3 += s14 * 470296;
        s4 += s14 * 654183;
        s5 -= s14 * 997805;
        s6 += s14 * 136657;
        s7 -= s14 * 683901;

        s1 += s13 * 666643;
        s2 += s13 * 470296;
        s3 += s13 * 654183;
        s4 -= s13 * 997805;
        s5 += s13 * 136657;
        s6 -= s13 * 683901;

        s0 += s12 * 666643;
        s1 += s12 * 470296;
        s2 += s12 * 654183;
        s3 -= s12 * 997805;
        s4 += s12 * 136657;
        s5 -= s12 * 683901;
        s12 = 0;

        carry0 = (s0 + (1 << 20)) >> 21;
        s1 += carry0;
        s0 -= carry0 << 21;
        carry2 = (s2 + (1 << 20)) >> 21;
        s3 += carry2;
        s2 -= carry2 << 21;
        carry4 = (s4 + (1 << 20)) >> 21;
        s5 += carry4;
        s4 -= carry4 << 21;
        carry6 = (s6 + (1 << 20)) >> 21;
        s7 += carry6;
        s6 -= carry6 << 21;
        carry8 = (s8 + (1 << 20)) >> 21;
        s9 += carry8;
        s8 -= carry8 << 21;
        carry10 = (s10 + (1 << 20)) >> 21;
        s11 += carry10;
        s10 -= carry10 << 21;

        carry1 = (s1 + (1 << 20)) >> 21;
        s2 += carry1;
        s1 -= carry1 << 21;
        carry3 = (s3 + (1 << 20)) >> 21;
        s4 += carry3;
        s3 -= carry3 << 21;
        carry5 = (s5 + (1 << 20)) >> 21;
        s6 += carry5;
        s5 -= carry5 << 21;
        carry7 = (s7 + (1 << 20)) >> 21;
        s8 += carry7;
        s7 -= carry7 << 21;
        carry9 = (s9 + (1 << 20)) >> 21;
        s10 += carry9;
        s9 -= carry9 << 21;
        carry11 = (s11 + (1 << 20)) >> 21;
        s12 += carry11;
        s11 -= carry11 << 21;

        s0 += s12 * 666643;
        s1 += s12 * 470296;
        s2 += s12 * 654183;
        s3 -= s12 * 997805;
        s4 += s12 * 136657;
        s5 -= s12 * 683901;
        s12 = 0;

        carry0 = s0 >> 21;
        s1 += carry0;
        s0 -= carry0 << 21;
        carry1 = s1 >> 21;
        s2 += carry1;
        s1 -= carry1 << 21;
        carry2 = s2 >> 21;
        s3 += carry2;
        s2 -= carry2 << 21;
        carry3 = s3 >> 21;
        s4 += carry3;
        s3 -= carry3 << 21;
        carry4 = s4 >> 21;
        s5 += carry4;
        s4 -= carry4 << 21;
        carry5 = s5 >> 21;
        s6 += carry5;
        s5 -= carry5 << 21;
        carry6 = s6 >> 21;
        s7 += carry6;
        s6 -= carry6 << 21;
        carry7 = s7 >> 21;
        s8 += carry7;
        s7 -= carry7 << 21;
        carry8 = s8 >> 21;
        s9 += carry8;
        s8 -= carry8 << 21;
        carry9 = s9 >> 21;
        s10 += carry9;
        s9 -= carry9 << 21;
        carry10 = s10 >> 21;
        s11 += carry10;
        s10 -= carry10 << 21;
        carry11 = s11 >> 21;
        s12 += carry11;
        s11 -= carry11 << 21;

        s0 += s12 * 666643;
        s1 += s12 * 470296;
        s2 += s12 * 654183;
        s3 -= s12 * 997805;
        s4 += s12 * 136657;
        s5 -= s12 * 683901;

        carry0 = s0 >> 21;
        s1 += carry0;
        s0 -= carry0 << 21;
        carry1 = s1 >> 21;
        s2 += carry1;
        s1 -= carry1 << 21;
        carry2 = s2 >> 21;
        s3 += carry2;
        s2 -= carry2 << 21;
        carry3 = s3 >> 21;
        s4 += carry3;
        s3 -= carry3 << 21;
        carry4 = s4 >> 21;
        s5 += carry4;
        s4 -= carry4 << 21;
        carry5 = s5 >> 21;
        s6 += carry5;
        s5 -= carry5 << 21;
        carry6 = s6 >> 21;
        s7 += carry6;
        s6 -= carry6 << 21;
        carry7 = s7 >> 21;
        s8 += carry7;
        s7 -= carry7 << 21;
        carry8 = s8 >> 21;
        s9 += carry8;
        s8 -= carry8 << 21;
        carry9 = s9 >> 21;
        s10 += carry9;
        s9 -= carry9 << 21;
        carry10 = s10 >> 21;
        s11 += carry10;
        s10 -= carry10 << 21;

        final byte[] result = new byte[32];
        result[0] = (byte) (s0);
        result[1] = (byte) (s0 >> 8);
        result[2] = (byte) ((s0 >> 16) | (s1 << 5));
        result[3] = (byte) (s1 >> 3);
        result[4] = (byte) (s1 >> 11);
        result[5] = (byte) ((s1 >> 19) | (s2 << 2));
        result[6] = (byte) (s2 >> 6);
        result[7] = (byte) ((s2 >> 14) | (s3 << 7));
        result[8] = (byte) (s3 >> 1);
        result[9] = (byte) (s3 >> 9);
        result[10] = (byte) ((s3 >> 17) | (s4 << 4));
        result[11] = (byte) (s4 >> 4);
        result[12] = (byte) (s4 >> 12);
        result[13] = (byte) ((s4 >> 20) | (s5 << 1));
        result[14] = (byte) (s5 >> 7);
        result[15] = (byte) ((s5 >> 15) | (s6 << 6));
        result[16] = (byte) (s6 >> 2);
        result[17] = (byte) (s6 >> 10);
        result[18] = (byte) ((s6 >> 18) | (s7 << 3));
        result[19] = (byte) (s7 >> 5);
        result[20] = (byte) (s7 >> 13);
        result[21] = (byte) (s8);
        result[22] = (byte) (s8 >> 8);
        result[23] = (byte) ((s8 >> 16) | (s9 << 5));
        result[24] = (byte) (s9 >> 3);
        result[25] = (byte) (s9 >> 11);
        result[26] = (byte) ((s9 >> 19) | (s10 << 2));
        result[27] = (byte) (s10 >> 6);
        result[28] = (byte) ((s10 >> 14) | (s11 << 7));
        result[29] = (byte) (s11 >> 1);
        result[30] = (byte) (s11 >> 9);
        result[31] = (byte) (s11 >> 17);

        return new Ed25519EncodedFieldElement(result);
    }

    private static long threeBytesToLong(final byte[] in, int offset) {
        int result = in[offset++] & 0xff;
        result |= (in[offset++] & 0xff) << 8;
        result |= (in[offset] & 0xff) << 16;
        return result;
    }

    private static long fourBytesToLong(final byte[] in, int offset) {
        int result = in[offset++] & 0xff;
        result |= (in[offset++] & 0xff) << 8;
        result |= (in[offset++] & 0xff) << 16;
        result |= in[offset] << 24;
        return ((long) result) & 0xffffffffL;
    }

    @Override
    public int hashCode() {
        return Arrays.hashCode(this.values);
    }

    @Override
    public boolean equals(final Object obj) {
        if (!(obj instanceof Ed25519EncodedFieldElement)) {
            return false;
        }

        final Ed25519EncodedFieldElement encoded = (Ed25519EncodedFieldElement) obj;
        return 1 == ArrayUtils.isEqualConstantTime(this.values, encoded.values);
    }

    @Override
    public String toString() {
        return HexEncoder.getString(this.values);
    }
}
